Q. 19 In the following exercises, fact... [FREE SOLUTION]

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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 6: Q. 19 (page 572)

In the following exercises, factor the greatest common factor from each polynomial.
$5 x^{3} - 15 x^{2} + 20 x$

Short Answer

Expert verified

The factored form is $\begin{array}{rcl} 5 x (x^{2} - 3 x + 4) \end{array}$ .

Step by step solution

Step 1. Given Information

The given polynomial is $5 x^{3} - 15 x^{2} + 20 x$ .

Step 2. Find the GCF of the terms

Factor each of the terms in the given expression.

$\begin{array}{rcl} 5 x^{3} & = & 5 路 x 路 x 路 x \\ 15 x^{2} & = & 5 路 3 路 x 路 x \\ 20 x & = & 2 路 2 路 5 路 x \end{array}$

From the obtained factors, it is observed that the common factors are $5, x$ .
Multiply the common factors.

$5 路 x = 5 x$

So, the GCF of the terms of the given expression is $5 x$ .

Step 3. Rewrite the given expression

Express each of the term of the given expression as a product of GCF, $5 x$ .

$5 x 路 x^{2} - 5 x 路 3 x + 5 x 路 4$

Use the reverse distributive property, $a b + a c = a (b + c)$ to rewrite the obtained expression.

role="math" localid="1644581217189" $5 x 路 x^{2} - 5 x 路 3 x + 5 x 路 4 = 5 x (x^{2} - 3 x + 4)$

Step 4. Check

Multiply the obtained factors.

$\begin{array}{rcl} 5 x (x^{2} - 3 x + 4) & = & 5 x 路 x^{2} - 5 x 路 3 x + 5 x 路 4 \\ = & 5 x^{3} - 15 x^{2} + 20 x \end{array}$

Since the obtained expression is the same as the given expression, the obtained factors are verified.

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91影视

In the following exercises, factor the greatest common factor from each polynomial.
$5 x^{3} - 15 x^{2} + 20 x$

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Find the GCF of the terms

Step 3. Rewrite the given expression

Step 4. Check

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91影视

In the following exercises, factor the greatest common factor from each polynomial. 5x3-15x2+20x

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Find the GCF of the terms

Step 3. Rewrite the given expression

Step 4. Check

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Geometry

Pure Maths

Logic and Functions

Theoretical and Mathematical Physics

Probability and Statistics

Study anywhere. Anytime. Across all devices.

In the following exercises, factor the greatest common factor from each polynomial.
$5 x^{3} - 15 x^{2} + 20 x$